Design considerations for robotically assembled through-tenon timber joints

This research investigates the robotic assembly of timber structures connected by wood–wood connections. As the digitization of the timber construction sector progresses, digital tools, such as industrial robotic arms and Computer Numerical Control machines, are becoming increasingly accessible. The new-found ease with which wood can be processed stimulates a renewed interest in traditional joinery, where pieces are simply interlocked instead of being connected by additional metallic parts. Previous research established a computational workflow for the robotic assembly of timber plate structures connected by wood–wood connections. This paper focuses on determining the physical conditions that allow inserting through-tenon joints with a robot. The main challenge lies in minimizing the clearance between the tenon and the mortise in order to keep the connections as tight as possible. An experimental protocol has, therefore, been developed to quantitatively assess the performance of the insertion according to different geometric parameters. Robotic insertion tests have been carried out on over 50 samples of 39 mm Laminated Veneer Lumber. Results showed the interest of tapering the joint with a 5 degrees angle, in addition to introducing an offset of 0.05 mm, to minimize friction forces during the insertion. This configuration was confirmed by successfully assembling a 2,50 m long box girder with the same parameters.


Introduction
The digitization of the timber construction sector is one of the key factors to reduce the embodied carbon in buildings and ultimately lower carbon emissions in the built environment (Reyes et al. 2021). In the last two decades, technological advances have enabled the spread of Computer Numerical Control (CNC) machines and engineered wood products, such as Cross and Glued Laminated Timber (CLT and Glulam). Those innovations favor a return to wood construction after a century focusing mainly on two mineral materials: concrete and steel. Aside from environmental considerations, another main advantage of contemporary timber constructions lies in the ease of prefabrication relying on standardized elements. Indeed, this reduced construction time leads to cost-competitive solutions (Hildebrandt et al. 2017).
However, many challenges remain for the sector to have the capacity to increase its market share largely covered by mineral materials, particularly with the expected growth in housing demand (United Nations Environment Programme 2020). Therefore, timber construction companies have started to investigate the use of Industrial Robotic Arms (IRA) to automate part of their workflow and increase their productivity. The main application is the robotic assembly of timber frame structures, as it is the most widespread timber construction system (Dangel 2016). Panels and studs are first placed on an inclined plane with a vacuum gripper equipped on the robot end effector. Then, the elements are fixed using a pneumatic nail gun (see Fig. 1).
This research aims at proposing an alternative to standard timber frame structures by replacing the screws with through-tenon joints and the beams with largely available wood-engineered panels that can be more easily processed by a CNC machine (Open Systems Lab 2012). This solution offers three advantages. First, it reduces the number of steps in the prefabrication process as the joints provide both a guide for the assembly and a means to connect the elements. Second, it decreases the embodied carbon of the construction system by avoiding metallic connectors (Fang et al. 2021). Third, it increases the structural performance by geometrically interlocking the pieces through form closure (Gamerro et al. 2020a, b).
However, inserting timber joints with a robotic arm is more difficult than nailing as tolerances are much smaller. Indeed, with too much clearance between the tenon and the mortise, the joint is loose and it reduces the rigidity of the connection. With too little clearance, it hinders the insertion of the joint, either partially or completely as friction forces exceed the robot threshold. Therefore, this experimental study focuses on determining the adequate design for the geometry of the joints that would make the robotic insertion of through-tenon joints possible.

State of the art
The problem of inserting one part into another with a robotic arm dates back to the early days of robotics. A classic example extensively covered in the literature is peg-in-hole insertion. Existing strategies generally rely on an initial robot trajectory that spirals around the hole (Suárez-Ruiz 2018) In addition, a force and torque sensor allows for adjusting the trajectory in real-time by comparing the data to a predetermined force pattern (Tang et al. 2016). Most recent works also integrate reinforcement learning algorithms to improve the reliability of the insertion (Gullapalli et al. 1994). However, the objects concerned are generally small, cylindrical, and smooth (made out of metal or plastic). Conversely, timber pieces are large, with more complex geometries, and a relatively rough surface. It is, therefore, harder to predict and interpret the force patterns to correctly adjust the robot trajectory.
Reinforcement learning and force sensors were also used by Apolinarska et al. (2021) to automate the insertion of half-lap joints. A virtual robot was first trained in simulation, so that the real robot could learn how to compensate for translational and rotational offsets. Although the results were promising, tight-fitting joints with a clearance inferior to 1 mm could not be inserted due to the limitations of the setup. An alternative method for training a robot was also proposed by Kramberger et al. (2022). Relying on the principles of Learning from Demonstration (LfD), the robot was taught how to insert half-lap joints by first analyzing the motion and force pattern of hand-guided examples. Both training methods make the insertion more reliable by compensating for potential misalignment. However, it is still necessary to add a considerable amount of clearance to ensure the robotic insertion.
To eliminate gaps and overcome induced friction forces, Robeller et al. exploited the elastic properties of wood through snap-fit joints (Robeller et al. 2017). As those joints can slightly bend, it makes it possible to insert oversized tenons without requiring too much force. However, the experiments highlighted the difficulties of inserting several joints at the same time. Despite the presence of a vibration device on the robot end effector, the sum of the resulting friction forces was too high and the joints required manual hammering to be inserted. In addition, the bending properties of snap-fit joints are conditioned by their small cross section which considerably reduces the shear resistance of the connection.
Another strategy consists in increasing the force of the robot end effector. Remote-controlled robotic clamps were developed by Leung et al. for the insertion of half-lap joints (Leung et al. 2021). The clamps can detach from the robot and synchronously apply a 3 kN force. The main advantage is that the strength or number of clamps can be increased to meet the required insertion force. However, the industrial implementation of this solution is constrained by the development of those specific pieces of hardware and by its limited application to timber beams connected by half-lap joints.
Most of the existing research on the topic has explored solutions based on software or hardware development. This paper proposes a more low-tech approach focusing on the joints themselves. A testing protocol to assess the performance of the robotic insertion is presented in Sect. 3. The results of the experiments on small and large samples are reported in Sect. 4. Finally, the influence of the geometric parameters on the progression of friction forces is discussed in Sect. 5.

Experimental setup
The experiments were all conducted with a 6-axis robotic arm (ABB 6400R/2.5-200) (ABB Product Specification IRB 6400R 2022) equipped with two vacuum grippers capable of lifting timber panels up to 200 kg for a maximum reach of 3 m. In addition, a custom testing setup was developed to measure the performance of the robotic insertion (see Fig. 2). A concrete block covered with a dense timber board was used as a flat and stable base on which to execute the robotic assembly. A square corner enables the precise positioning of the male piece before it is picked by the robot, while the female piece is clamped inside a reserved hollow socket. The position of both pieces relative to the robot frame is, therefore, known with a tolerance inferior to one millimeter.
To measure the reaction forces during the insertion, a 6-axis force/torque sensor (Schunk, FT Omega160) was attached to the robot end effector. Besides, two Linear Variable Differential Transformers (LVDT) were fixed on the male piece to measure the vertical displacement and report eventual rotations in the plane of the inserted piece. Finally, the presence of a cavity under the female piece should also be noted. This prevents any contact between the tenons and the support and avoids interfering reaction forces.

Experimental parameters
Fixed and variable experimental parameters are reported in Table 1 and represented in Fig. 3. It was decided to work   with 39 mm thick spruce Laminated Veneer Lumber (LVL) panels as this is a commonly used product in the timber construction sector. Its high strength-to-weight ratio makes it indeed an ideal material for load-bearing applications and one of the objectives of the study was to get as close as possible to real industry conditions. However, to avoid wasting wood, the dimensions of the samples were kept to a minimum by matching the size of the robot end effector and performing the tests with only one vacuum gripper. Hardwood panels were not investigated in this research as they are less used in construction for now. The robot speed was set to 1 mm/s during the insertion. While this is relatively slow in comparison with industrial standards, this allowed a better assessment of the influence of the shape of the connections on the robotic insertion. Besides, by working at reduced speed, we place ourselves in the most unfavorable case as we no longer benefit from the acceleration of the robot when inserting the joint.
Regarding the parameters associated with the geometry of the mortises and the tenons, a length of 100 mm and a minimum distance of 50 mm from the edge of the board have been set for all joints. This follows the design guidelines provided by Gamerro et al. for orthogonal timber slabs connected by mortise and tenon joints (Gamerro 2020). Therefore, the remaining variable parameters of the experimental campaign were the offset, the angle, the number of joints, and the size of the chamfer.

Fabrication of the samples
The geometry of the joints was parametrically generated using the grasshopper plugin Manis . The plugin also allowed to generate the fabrication files and the robotic trajectories for the subsequent insertion tests. All samples were then cut with a 5-axis CNC machine. However, only those with an angle parameter greater than 0 degrees actually required 5-axis machining, whereas 3-axis machining was sufficient for the other samples. In addition, the introduction of this bevel required to mill the four faces of the tenons. This implies flipping the piece on the CNC table and repositioning them with a corner square to mill the side of the tenon that was previously facing the table. Table 2 shows that the fabrication time for joints requiring 5-axis milling is increased by 30 to 40% compared to 3-axis. Calculations include both drilling and cutting steps. The time for flipping the pieces is also taken into account and was measured at 1 min per sample on average.
Fabrication tolerance is one of the main challenges for the robotic insertion of timber joints. While our CNC is accurate to within 0.05 mm, irregularities in the interface between the martyr table and the panel can reduce the accuracy of the cut in the vertical axis to approximately 0.25 mm. The thickness of the panels can also vary by about 1 mm depending on production and storage conditions. Therefore, to compensate for material tolerances, the female pieces, as well as the tenons of the male pieces, were surfaced to 38 mm. To  avoid potential dimensional variations induced by external factors, the pieces were assembled directly after being cut. Figure 4 summarizes the dimensional tolerances obtained after CNC machining.

Experimental protocol
After fabrication, each sample was brought to the insertion table (Fig. 5(1)) and tested with the robotic arm. The male and female pieces were first positioned in their dedicated slots (Fig. 5(2)). Then, the male piece was lifted by the vacuum gripper (Fig. 5(3)) and rotated 38 mm above the female piece (Fig. 5(4)). Next, the two LVDTs were attached and centered on the most extreme tenons (Fig. 5(5)).
To compare the progression of the insertion for different samples, the precise height of the starting point of each test was measured. It was obtained by controlling the distance between the male and female pieces with each LVDT and averaging both values. In addition, using two distance sensors allowed for measuring the rotation of the male piece in its plane which could reach up to 2 degrees. However, this variation remained negligible as the male piece would always align itself with the female piece during the insertion of the joints.
Before initiating the data recording, all sensors were reset and the synchronization of the measurements between the force sensor and the LVDTs was ensured. Finally, the robotic insertion was started. In order to prevent the robot from stopping the insertion too early due to frictional forces, the final point of the robot path was shifted 5 mm lower for all tests. Once the insertion was completed (Fig. 5(6)), the male part was removed and reinserted two more times to investigate possible variations in the results. However, only the first insertion was considered for the final result. Taking into account the overall tolerances of the machining and panels, the insertion was considered complete if the tenon was at least 95% inserted into the mortise. This corresponds to a traveled distance of 36 mm out of the total 38 mm of the total plate thickness. Complete insertions were also confirmed by visual inspection and manual measurement at the end of each test.

Offset parameter
The first experiments focused on studying the influence of the offset parameter (see Fig. 3). The percentage of insertion and the maximum friction forces are reported, respectively, in Tables 3 and 4. Detailed graphs are reported in Appendix A. In this configuration, the threshold force for the robot varies between 1700 N and 2100 N. Under 0.10 mm of offset, the robot detected a collision almost instantaneously. For 0.10 mm and 0.15 mm, the robot managed to insert the tenons about halfway through the mortise before the forces were too high. From 0.2 mm, recorded forces did not exceed 1500 N and the insertion was fully achieved. However, with this amount of clearance, the joints were already considerably loose. It was observed that the pieces could rotate freely in a range of about 3 degrees leading to potentially large discrepancies during the assembly.

Chamfer and offset parameter
For the second batch of tests, the four edges of the mortises were chamfered on a distance of 5 mm (see Fig. 3). This value was chosen based on previous research work showing that a chamfer of 5 mm at a 45 degrees angle was sufficient to compensate for robot positioning errors ). In addition, a chamfer was applied on the tenon but   only on the smaller sides, as shown in Fig. 3. This removes the need to flip the tenon plate during fabrication to chamfer the side facing the CNC table. This new feature allowed to insert a 2 tenons plate with an offset parameter of 0.10 mm instead 0.20 mm (see Table 5). The chamfer reduces the risk of blocking situations and helps to guide the tenon into the mortise in case of initial misalignment. Figure 6 shows the linear progression of the frictional forces during the insertion with 0.05 mm and 0.10 mm of offset. For 0.05 mm, the robot stopped at about one-third of the mortise as it reached a force of 1800 N. For 0.10 mm, a first spike can be observed around 15%. This is where the tenon hit the chamfer before sliding into the mortise.

Angle parameter
While combining a 5 mm chamfer and 0.10 mm offset allows the insertion of a plate with 2 tenons, the required force increases with the number of tenons. To avoid introducing more clearance and loosening the connection, another solution based on the tapering of the joint was investigated (see angle parameters in Fig. 3). Taper angles ranging from 1 to 15 degrees were applied on 4 faces of the tenons and the mortises. This required cutting the joints in 5-axis and to flip the tenon plate on the CNC table to mill the bottom face of the panel. This bevel angle has the advantage of minimizing friction during most of the insertion. Indeed, even with a small angle of 1 degree, forces rose only after 60% of insertion (see Fig. 7). However, as the space between the mortise and the tenon shrinks until reaching 0 mm at 100% of insertion (see Fig. 8), forces rise abruptly during the last millimeters. This prevented the robot to progress further than 80 to 95% for all tested angles (see Table 6). Nevertheless, completely eliminating the clearance has the advantage of improving the rigidity of the connection compared to previous results obtained by varying the offset parameter. Finally, for an angle parameter larger than 5 degrees, no significant gain in the assembly insertion was achieved.

Combined parameters
The bevel angle alone does not allow the full insertion of the joints. Therefore, we studied if combining the offset and angle parameters could solve this issue. The angle was set to 5 degrees for all tests as it scored best in the previous series. Results for the insertion of 2 to 5 tenons with an angle of 5 degrees and an offset of 0.05, 0.10, and 0.15 mm are shown in Table 7. Corresponding maximum forces are also reported in Table 8 and detailed graphs are available in Appendix B. We observed that only a minimal amount of offset is required as, with 0.05 mm, all tests were successfully inserted. Besides, the number of tenons no longer seems to affect the performance of the insertion. While for 5 tenons and 0.15 mm offset, the insertion was slightly under the threshold value, results for 0.05 mm and 0.10 mm showed that 5 tenons can be fully inserted with the same parameters as for 2, 3, and 4 tenons.

Extrapolation to a box girder
Previous tests carried out on 80 cm long samples showed that an angle of 5 degrees and an offset of 0.05 mm enabled the robotic insertion of 2 to 5 tenons. To determine whether this would work for larger pieces, with a greater number of tenons, and for other robotic configurations, the assembly of a 250 cm long box girder was performed with the robot (see Fig. 9). The girder was made out of two vertical webs and two horizontal flanges. Each panel was connected by 8 through-tenon joints with chamfers of 5 by 5 mm, an offset of 0.05 mm, and an angle of 5 degrees. The position of the bottom flange was manually referenced in the robot space. Then, both webs were assembled following a similar protocol as for smaller samples. LVDTs were attached to the first and last tenons of the plate (Fig. 9, left). For the top flange, the situation was different. First, mortises were inserted into the tenons instead of the opposite. Therefore, LVDTs were again attached to the webs and placed in the upward direction on opposite tenons (Fig. 9, right). Second, the orientation of the reaction force compared to the vacuum gripper was changed  . 9 Robotic assembly of a box girder. The four plates are connected by eight through-tenon joints each 1 3 from tangential to normal. Third, two plates needed to be simultaneously inserted. Finally, while 8 and 16 joints needed to be simultaneously assembled for the webs and the top flange, respectively, the robotic insertion of the three plates was successful. We noted that, in this configuration, measured forces could reach 3000 N without triggering collision detection. This is because the robot is working at a closer range and can, therefore, take higher loads. However, as the last part of the insertion curves in Fig. 10 is almost vertical, the effective insertion of each plate actually required about half of the maximum force.

Conclusions
This experimental study allowed the identification of optimal design parameters for through-tenon joints assembled by a robotic arm. The main issue at stake consisted in finding a balance between the rigidity of the connections and the ease of assembly for the robot. The augmentation of the required force when assembling multiple joints simultaneously was considered a major challenge by previous research work. Standard industrial robotic arms are indeed quite limited in the force they can apply before detecting a collision. The tests carried out allowed the development of a precise protocol to quantitatively compare the insertion performance for different geometric parameters. This included the influence of 3-axis offset and 5-axis bevel angles, as well as the presence of chamfers.
The results indicate that the offset parameter alone considerably reduces the rigidity of the connections. Nevertheless, it has the advantage of keeping the manufacturing process in 3-axis, which might be appreciated in smaller industries, where 5-axis cutting is not always available. In such case, our experiments show that, between 2 and 5 tenons, an offset of at least 0.2 mm should be applied to ensure the robotic assembly. However, this number could be revised upward for larger numbers of tenons as the reaction forces could increase with the number of tenons.
Specific CNC milling bits with a 45 degrees angle can also be used to chamfer the edges of the joint while remaining in 3-axis. A 5 by 5 mm chamfer will reduce blocking situations and help to guide the tenon inside the mortise. It makes it possible to insert 2 tenons with an offset of only 0.10 mm.
To insert a wide configuration of tenons without loosening too much the connections, we investigated the tapering of the joints in 5-axis. We demonstrated that the offset parameters can be reduced to 0.05 mm by combining a bevel angle of 5 degrees and a chamfer of 5 mm. The conic shape eliminates friction forces during most of the insertion and ultimately reduces the clearance. The assembly of a 2.5 m long box girder, with up to 16 joints that needed to be assembled at the same time, confirmed that this combination of parameters was optimal for the robotic assembly of large-scale timber plate structures.
Further investigations would be needed to extend the design guidelines depending on the types of panels, wood species, and the size of the elements. While the current study focused on the insertion of spruce LVL panels, it is expected that the resulting friction forces will be different for Cross-Laminated Timber (CLT) and Oriented Strand Board (OSB) panels which are also commonly used in construction. The choice of panel types and tree species will influence the texture and hardness of the wood. The use of a softer wood will tend to increase the tolerance and facilitate the insertion. Similarly, smooth surfaces will more easily slide against each other. A quantitative analysis of these phenomena would, therefore, be an interesting complement to this research.
Furthermore, the influence of humidity and temperature on the joints has been excluded from the study so far. As the samples were assembled with the robotic arm right after being cut with the CNC, potential deformations due to those environmental factors could be neglected. However, future research could focus on assessing the validity of the findings if the samples were affected by dimensional variations. Hygroscopic swelling could also be exploited by performing the robotic insertion with a low level of To conclude, this research paves the way for the automated assembly of structures connected by wooden joints. It provides an alternative to existing nailing and gluing methods for timber framing. While further research needs to be carried out to extend this technique to industrial processes and assess its performance, the establishment of design guidelines as well as the development of a testing methodology is a substantial achievement toward its application to real case studies.